Gene mapping, linkage analysis and computational challenges. Konstantin Strauch

Transcription

1 Gene mapping, linkage analysis an computational challenges Konstantin Strauch Institute for Meical Biometry, Informatics, an Epiemiology (IMBIE) University of Bonn

2 Genetics an inheritance 23 chromosomes in humans (22 autosomes, 1 sex chro.), an iniviual carries two copies of each sort (father/mother) Genetic locus: refers to certain position on a chromosome Alleles: ifferent possible DNA variants at a certain locus Inheritance at single locus: Two genetic loci on ifferent chromosomes: Alleles at both loci segregate inepenently (Menel s thir law)

3 Meiosis an recombination Two homologous chromosomes in a parent A1 A2 A1 A2 A1 A2 B1 B2 B1 B2 B1 B2 C1 C2 C2 C1 C2 C1 Chiasmata (i.e., crossovers) lea to recombinations between loci (e.g., here, between loci B an C). A recombination becomes more likely if two genetic loci are more istant. inherite to chil

4 Linkage analysis: the basic concepts Look for co-segregation between marker(s) an trait locus within families Parametric (moel-base) analysis or LOD-score analysis: calculation of likelihoo L = P (observe ata moel), isease moel parameters must be explicitly specifie. Simplest case of one iallelic trait locus (alleles +, m): - isease allele frequency p - three penetrances {f +/+,f Het,f m/m } Penetrance: Probability of an iniviual being affecte given a certain genotype at isease locus

5 Mapping a isease locus by linkage analysis Typing of polymorphic markers an analysis of co-segregation of marker alleles an isease m m m m1 + 3 NR NR R NR NR NR Parametric analysis uner a ominant moel {f +/+,f Het,f m/m } = {0,1,1} 5 meioses nonrecombinant, 1 meiosis recombinant recombination fraction estimate: θ = 1/6 = The result strongly epens on the assume trait moel. - Simple situation! Nee likelihoo calculation if ifmore complex.

6 Multi-marker analysis Multi-marker analysis, multipoint analysis Jointly use several markers on a chromosome for an analysis; all genetic istances between the marker loci must be known. Goal: mapping of the isease locus (with unknown position) relative to the fixe map of markers (known positions) Avantage over single-marker analysis: If Ifa person is uninformative for a marker, linkage information can at least partly reconstructe by ajacent markers. This is particularly important for genetic markers for which the information content is small, such as single nucleotie polymorphisms (SNPs).

7 Likelihoo calculation General formulation of the likelihoo: L = g G Sum over all possible genotype combinations! i P ( xi gi) P( gi) Pθ penetrances i F i F genotype frequencies ( g x i : phenotypes (marker an trait) for person i g i : orere multilocus genotype for person i Calculation becomes extremely complicate, especially with many iniviuals, many genetic loci, an in case of missing information. i g p i, transmission probabilities g m i )

8 Complexity of the calculations Example: 10 possible genotypes at each locus 4 loci 10,000 multilocus genotypes 8 loci 100,000,000 multilocus genotypes Proceure: combination of ientical terms omission of terms equal to zero Different algorithmic approaches an computational nees: Elston-Stewart algorithm (Hum Here 21: , 1971) linear in # of persons, exponential in # of markers Laner-Green algorithm (PNAS 84: , 1987) linear in # of markers, exponential in # of persons Bayesian networks: flexibly orer calculations (Fishelson & Geiger, Bioinformatics 18 Suppl:S189-S198, 2002)

9 The principle of GENEHUNTER (Kruglyak et al., AJHG 1996) I. Extract the inheritance information from the markers; fin the probability istribution of the inheritance vectors (given all marker ata) for many positions along the II. chromosome P ( V ( x) = w) inheritance vector: contains one bit for each meiosis, etermines whether the paternally ( 0 ) or maternally ( 1 ) inherite allele has been transmitte Score the ifferent positions (for the putative trait locus) accoring to the trait phenotypes ( S w, φ ) S: isease locus likelihoo for parametric linkage analysis; yiels the LOD score III. Take the expecte value ( S( x) S w, φ ) P( V ( x) = w) = w V

10 Complex traits: two-trait-locus analysis Parametric (LOD-score) analysis with two isease loci: tests specific two-trait-locus moels Many parameters: - 2 isease allele frequencies - 9 penetrances Two-locus penetrances First locus +/+ Het m/m Secon locus +/+ Het m/m f 00 f 01 f 02 f 10 f 11 f 12 f 20 f 21 f 22 Two-trait-locus analysis has higher power to etect linkage Genetic regions can be localize more accurately Information can be gaine about how two loci act / interact

11 GENEHUNTER (written in C) with one an two trait loci Complete formulation for a single trait locus: ( ) S( x) = S φ ( w, ) P( V ( x) = w) - with S w, φ efine as the isease-locus likelihoo, this yiels the stanar LOD score (one trait locus). Extension for two trait loci: GENEHUNTER-TWOLOCUS (Strauch et al., Am J Hum Genet 66: ): S( x1, x 2 ) = = w1, w2 V w1, w2 V Assumption: both isease loci are unlinke (inepenence) w V ( ) 1, w2, φ PV ( ( x1) = w1, V( x2) = w2) S w ( ) 1, w2, φ PV ( ( x1) = w1 ) PV ( ( x2) = w2) S w

12 GENEHUNTER-TWOLOCUS: optimization of the coe Since the scoring function S(w 1,w 2 ) now is a matrix, calculation takes longer than with the single-trait-locus GENEHUNTER versions (uses >95% of computing time!) - up to now, # of effective meioses (i.e., bits ) 12 13, even on machines like the SunFire SMP Cluster Aachen Technical optimization of critical parts of the algorithm: Extraction of loop-invariant coe Replacement of case constructs by bit operations Loop interchange to improve loop unrolling Subroutine inlining Spee-up by a factor of 14 (one orer of magnitue!)

13 GENEHUNTER-TWOLOCUS: parallelization The two-trait-locus LOD score is calculate as: ( w ) 1, w2, φ P( V ( x1) = w1) P( V ( x2 = 2) S( x1, x2) = S ) w w1, w2 V S( x1, x2) = S w1, w2, P V ( x1) w1 P V ( x2 φ = ) = w w2 V w 1 V ( ) ( ) ( 2) Calculate w 1 V ' ( w1, w2, φ ) P( V ( x1) = w1) : S ( w2) x 1 S = in parallel! No inter-processor communication, ieal loa balancing linear spee-up; 1/n time with n processors GH-TWOLOCUS: now analyze peigrees with 17 bits

14 GENEHUNTER-TWOLOCUS: application to hypercholesterolemia Family of of consierable size (17 effective meioses, bits ) Estimate computation time with ol version: 3 years Computation time with new version: ays Computations one with the SunFire SMP Cluster Aachen Only if if two mutant alleles are present both at at a locus on on chromosome 1 an at at a locus on on chromosome 13, the person will express hypercholesterolemia. (multiplicative moe of of interaction)

15 GENEHUNTER-TWOLOCUS: optimize an parallelize version Johannes Dietter, Alexaner Spiegel, Dieter an an Mey, Hans-Joachim Pflug, Hussam Al-Kateb, Katrin Hoffmann, Thomas F Wienker, Konstantin Strauch: Efficient two-trait-locus linkage analysis through program optimization an parallelization: application to to hypercholesterolemia. European Journal of of Human Genetics 12: , 2004.

16 GENEHUNTER-TWOLOCUS: application to high factor VIII levels

17 People Johannes Dietter Dieter an Mey Alexaner Spiegel Hans-Joachim Pflug (IMBIE, Bonn) (Center for Computing an Communication, RWTH Aachen) Thank you!